Question

If sides of the triangle are 195 m ,180m,75m and then area of triangle .........​

Answer 1

Answer:

Perimeter of the triangle = 450m

➡ It's semi-perimeter = 450/2 = 225m

Ratio between the sides of the triangle is 13 : 12 : 5

Let the sides of the triangle be 13x, 12x and 5x respectively.

We know that,

Perimeter of a triangle = sum of all three sides

➡ 13x + 12x + 5x = 450m

➡ 30x = 450m

➡ x = 450/30

➡ x = 15m

The sides of the triangle are :-

13x = 13 × 15 = 195m

12x = 12 × 15 = 180m

5x = 5 × 15 = 75m

Area of the triangle by heron's formula :-

= √[s(s - a)(s - b)(s - c)] (s = semi-perimeter, a, b and c are the sides respectively)

= √[225(225 - 195)(225 - 180)(225 - 75)

= √(225 × 30 × 45 × 150)

= √(3 × 3 × 5 × 5 × 2 × 3 × 5 × 3 × 3 × 5 × 2 × 3 × 5 × 5)

= √(3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5 × 5 × 5 × 5 × 2 × 2)

= 3 × 3 × 3 × 5 × 5 × 5 × 2

= 6750m²

Now, we've to find the shortest altitude of the triangle.

We also know that,

Area of a triangle = 1/2 × base × height

When base = 195m, 1/2 × 195 × h = 6750m²

➡ h = 6750/1 × 2/195 = 69m (approx)

When base = 180m, 1/2 × 180 × h = 6750m²

➡ h = 6750/9 = 75m

When base = 75m, 1/2 × 75 × h = 6750m²

➡ 6750/37.5 = 180m

Hence, the smallest altitude is 69m.

Answer 2

Answer:

6750 m^2

Step-by-step explanation:

Let the sides be

a = 195 m

b = 180 m

c = 75 m

Now, semiperimeter, s = perimeter/2

= (a + b + c)/2

= (195 + 180 + 75)/2

= 450/2

= 225 m

So, by using Heron's formula, area is:

A = root[s(s-a)(s-b)(s-c)]

= root[225 x 30 x 45 x 150]

= 6750 m^2